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Király B, Varga T, Szabó G, Garay J. Evolutionarily stable payoff matrix in hawk-dove games. BMC Ecol Evol 2024; 24:65. [PMID: 38769504 PMCID: PMC11107024 DOI: 10.1186/s12862-024-02257-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Accepted: 05/15/2024] [Indexed: 05/22/2024] Open
Abstract
BACKGROUND Classical matrix game models aim to find the endpoint of behavioural evolution for a set of fixed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players' strategies but also the payoff matrix evolves according to natural selection. RESULTS We start out from the hawk-dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifies fighting ability and determines the probability of winning and the cost of losing escalated hawk-hawk fights. We define evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payoff matrix. CONCLUSIONS We find that the maximal possible cost of escalating fights remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the final evolutionarily stable phenotype maximizes the payoff of hawk-hawk fights. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.
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Affiliation(s)
- Balázs Király
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary.
| | - Tamás Varga
- Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., Szeged, H-6720, Hungary
| | - György Szabó
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
- Institute of Evolution, HUN-REN Centre for Ecological Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
| | - József Garay
- Institute of Evolution, HUN-REN Centre for Ecological Research, Konkoly-Thege Miklós út 29-33., Budapest, H-1121, Hungary
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2
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Ecotière C, Billiard S, André JB, Collet P, Ferrière R, Méléard S. Human-environment feedback and the consistency of proenvironmental behavior. PLoS Comput Biol 2023; 19:e1011429. [PMID: 37721943 PMCID: PMC10538744 DOI: 10.1371/journal.pcbi.1011429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Revised: 09/28/2023] [Accepted: 08/13/2023] [Indexed: 09/20/2023] Open
Abstract
Addressing global environmental crises such as anthropogenic climate change requires the consistent adoption of proenvironmental behavior by a large part of a population. Here, we develop a mathematical model of a simple behavior-environment feedback loop to ask how the individual assessment of the environmental state combines with social interactions to influence the consistent adoption of proenvironmental behavior, and how this feeds back to the perceived environmental state. In this stochastic individual-based model, individuals can switch between two behaviors, 'active' (or actively proenvironmental) and 'baseline', differing in their perceived cost (higher for the active behavior) and environmental impact (lower for the active behavior). We show that the deterministic dynamics and the stochastic fluctuations of the system can be approximated by ordinary differential equations and a Ornstein-Uhlenbeck type process. By definition, the proenvironmental behavior is adopted consistently when, at population stationary state, its frequency is high and random fluctuations in frequency are small. We find that the combination of social and environmental feedbacks can promote the spread of costly proenvironmental behavior when neither, operating in isolation, would. To be adopted consistently, strong social pressure for proenvironmental action is necessary but not sufficient-social interactions must occur on a faster timescale compared to individual assessment, and the difference in environmental impact must be small. This simple model suggests a scenario to achieve large reductions in environmental impact, which involves incrementally more active and potentially more costly behavior being consistently adopted under increasing social pressure for proenvironmentalism.
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Affiliation(s)
- Claire Ecotière
- Centre de Mathématiques Appliquées, CNRS, Ecole Polytechnique, IP Paris, Palaiseau, France
| | | | - Jean-Baptiste André
- Institut Jean Nicod, Département d’études cognitives, ENS, EHESS, PSL Research University, CNRS, Paris France
| | - Pierre Collet
- CPHT, CNRS, Ecole polytechnique, IP Paris, Palaiseau, France
| | - Régis Ferrière
- Institut de Biologie (IBENS), ENS-PSL, CNRS, INSERM, Paris, France
- Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona, United States of America
- iGLOBES International Research Laboratory, CNRS, ENS-PSL, University of Arizona, Tucson, Arizona, United States of America
| | - Sylvie Méléard
- Centre de Mathématiques Appliquées, CNRS, Ecole Polytechnique, IP Paris, Palaiseau, France
- Institut Universitaire de France, Paris, France
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3
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Roy S, Nag Chowdhury S, Kundu S, Sar GK, Banerjee J, Rakshit B, Mali PC, Perc M, Ghosh D. Time delays shape the eco-evolutionary dynamics of cooperation. Sci Rep 2023; 13:14331. [PMID: 37653103 PMCID: PMC10471784 DOI: 10.1038/s41598-023-41519-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 08/28/2023] [Indexed: 09/02/2023] Open
Abstract
We study the intricate interplay between ecological and evolutionary processes through the lens of the prisoner's dilemma game. But while previous studies on cooperation amongst selfish individuals often assume instantaneous interactions, we take into consideration delays to investigate how these might affect the causes underlying prosocial behavior. Through analytical calculations and numerical simulations, we demonstrate that delays can lead to oscillations, and by incorporating also the ecological variable of altruistic free space and the evolutionary strategy of punishment, we explore how these factors impact population and community dynamics. Depending on the parameter values and the initial fraction of each strategy, the studied eco-evolutionary model can mimic a cyclic dominance system and even exhibit chaotic behavior, thereby highlighting the importance of complex dynamics for the effective management and conservation of ecological communities. Our research thus contributes to the broader understanding of group decision-making and the emergence of moral behavior in multidimensional social systems.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, 700032, India
| | - Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA, 95616, USA
| | - Srilena Kundu
- Department of Ecology & Evolution, University of Chicago, Chicago, IL, 60637, USA
| | - Gourab Kumar Sar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore, 560029, India
| | - Biswambhar Rakshit
- Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 404332, Taiwan
- Alma Mater Europaea, Slovenska ulica 17, 2000, Maribor, Slovenia
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria
- Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India.
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4
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Jiang Y, Wang X, Liu L, Wei M, Zhao J, Zheng Z, Tang S. Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks. PLoS Comput Biol 2023; 19:e1011269. [PMID: 37379330 DOI: 10.1371/journal.pcbi.1011269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 06/13/2023] [Indexed: 06/30/2023] Open
Abstract
Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.
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Affiliation(s)
- Yishen Jiang
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Xin Wang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Longzhao Liu
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
| | - Ming Wei
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
| | - Jingwu Zhao
- School of Law, Beihang University, Beijing, China
| | - Zhiming Zheng
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
| | - Shaoting Tang
- Institute of Artificial Intelligence, Beihang University, Beijing, China
- Key laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing, China
- State Key Lab of Software Development Environment (NLSDE), Beihang University, Beijing, China
- Zhongguancun Laboratory, Beijing, P.R.China
- Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing, China
- PengCheng Laboratory, Shenzhen, China
- Institute of Medical Artificial Intelligence, Binzhou Medical University, Yantai, China
- School of Mathematical Sciences, Dalian University of Technology, Dalian, China
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5
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Nag Chowdhury S, Banerjee J, Perc M, Ghosh D. Eco-evolutionary cyclic dominance among predators, prey, and parasites. J Theor Biol 2023; 564:111446. [PMID: 36868345 DOI: 10.1016/j.jtbi.2023.111446] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 02/24/2023] [Accepted: 02/25/2023] [Indexed: 03/05/2023]
Abstract
Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, CA 95616, USA
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore 560029, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia; Alma Mater Europaea, Slovenska ulica, 17, 2000 Maribor, Slovenia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria; Department of Physics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India.
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6
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Lamm E, Finkel M, Kolodny O. Human major transitions from the perspective of distributed adaptations. Philos Trans R Soc Lond B Biol Sci 2023; 378:20210401. [PMID: 36688390 PMCID: PMC9869454 DOI: 10.1098/rstb.2021.0401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Distributed adaptations are cases in which adaptation is dependent on the population as a whole: the adaptation is conferred by a structural or compositional aspect of the population; the adaptively relevant information cannot be reduced to information possessed by a single individual. Possible examples of human-distributed adaptations are song lines, traditions, trail systems, game drive lanes and systems of water collection and irrigation. Here we discuss the possible role of distributed adaptations in human cultural macro-evolution. Several kinds of human-distributed adaptations are presented, and their evolutionary implications are highlighted. In particular, we discuss the implications of population size, density and bottlenecks on the distributed adaptations that a population may possess and how they in turn would affect the population's resilience to ecological change. We discuss the implications that distributed adaptations may have for human collective action and the possibility that they played a role in colonization of new areas and niches, in seasonal migration, and in setting constraints for minimal inter-population connectivity. This article is part of the theme issue 'Human socio-cultural evolution in light of evolutionary transitions'.
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Affiliation(s)
- Ehud Lamm
- The Cohn Institute for History and Philosophy of Science and Ideas, Tel Aviv University, Tel Aviv 69978, Israel
| | - Meir Finkel
- The Cohn Institute for History and Philosophy of Science and Ideas, Tel Aviv University, Tel Aviv 69978, Israel
| | - Oren Kolodny
- Department of Ecology, Evolution, and Behavior, Institute for Life Sciences, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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7
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Roy S, Nag Chowdhury S, Mali PC, Perc M, Ghosh D. Eco-evolutionary dynamics of multigames with mutations. PLoS One 2022; 17:e0272719. [PMID: 35944035 PMCID: PMC9362954 DOI: 10.1371/journal.pone.0272719] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner’s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies.
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Affiliation(s)
- Sourav Roy
- Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
| | - Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Alma Mater Europaea, Maribor, Slovenia
- Complexity Science Hub Vienna, Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, West Bengal, India
- * E-mail:
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8
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Barfuss W, Mann RP. Modeling the effects of environmental and perceptual uncertainty using deterministic reinforcement learning dynamics with partial observability. Phys Rev E 2022; 105:034409. [PMID: 35428165 DOI: 10.1103/physreve.105.034409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Accepted: 02/24/2022] [Indexed: 11/07/2022]
Abstract
Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios, from navigation and foraging behavior to the provision of renewable resources and public infrastructures. Yet previous modeling work on agent learning and decision-making either lacks a systematic way to describe this source of uncertainty or puts the focus on obtaining optimal policies using complex models of the world that would impose an unrealistically high cognitive demand on real agents. In this work we aim to efficiently describe the emergent behavior of biologically plausible and parsimonious learning agents faced with partially observable worlds. Therefore we derive and present deterministic reinforcement learning dynamics where the agents observe the true state of the environment only partially. We showcase the broad applicability of our dynamics across different classes of partially observable agent-environment systems. We find that partial observability creates unintuitive benefits in several specific contexts, pointing the way to further research on a general understanding of such effects. For instance, partially observant agents can learn better outcomes faster, in a more stable way, and even overcome social dilemmas. Furthermore, our method allows the application of dynamical systems theory to partially observable multiagent leaning. In this regard we find the emergence of catastrophic limit cycles, a critical slowing down of the learning processes between reward regimes, and the separation of the learning dynamics into fast and slow directions, all caused by partial observability. Therefore, the presented dynamics have the potential to become a formal, yet practical, lightweight and robust tool for researchers in biology, social science, and machine learning to systematically investigate the effects of interacting partially observant agents.
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Affiliation(s)
- Wolfram Barfuss
- Institute for Theoretical Physics, University of Tübingen, 72076 Tübingen, Germany.,Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Richard P Mann
- Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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9
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Balasekaran M, Johanis M, Rychtář J, Taylor D, Zhu J. Quasi-neutral evolution in populations under small demographic fluctuations. J Theor Biol 2022; 538:111040. [DOI: 10.1016/j.jtbi.2022.111040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 01/11/2022] [Accepted: 01/19/2022] [Indexed: 10/19/2022]
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10
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McNamara JM. Game Theory in Biology: Moving beyond Functional Accounts. Am Nat 2021; 199:179-193. [DOI: 10.1086/717429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- John M. McNamara
- School of Mathematics, University of Bristol, Bristol BS8 1UG, United Kingdom
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11
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Chowdhury SN, Kundu S, Perc M, Ghosh D. Complex evolutionary dynamics due to punishment and free space in ecological multigames. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0397] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigmatic metaphors of social dilemmas with contrasting outcomes. We use the Prisoner’s Dilemma and Snowdrift games as the backbone of the proposed mathematical model. Since cooperation is a costly proposition in the face of the Darwinian theory of evolution, we go beyond the traditional framework by introducing punishment as an additional strategy. Punishers bare an additional cost from their own resources to try and discourage or prohibit free-riding from selfish defectors. Our model also incorporates the ecological signature of free space, which has an altruistic-like impact because it allows others to replicate and potentially thrive. We show that the consideration of these factors has broad implications for better understanding the emergent complex evolutionary dynamics. In particular, we report the simultaneous presence of different subpopulations through the spontaneous emergence of cyclic dominance, and we determine various stationary points using traditional game-theoretic concepts and stability analysis.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Alma Mater Europaea, Slovenska ulica, 17, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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12
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Park HJ, Gokhale CS, Bertels F. How sequence populations persist inside bacterial genomes. Genetics 2021; 217:6151697. [PMID: 33724360 PMCID: PMC8049555 DOI: 10.1093/genetics/iyab027] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 02/04/2021] [Indexed: 01/04/2023] Open
Abstract
Compared to their eukaryotic counterparts, bacterial genomes are small and contain extremely tightly packed genes. Repetitive sequences are rare but not completely absent. One of the most common repeat families is REPINs. REPINs can replicate in the host genome and form populations that persist for millions of years. Here, we model the interactions of these intragenomic sequence populations with the bacterial host. We first confirm well-established results, in the presence and absence of horizontal gene transfer (hgt) sequence populations either expand until they drive the host to extinction or the sequence population gets purged from the genome. We then show that a sequence population can be stably maintained, when each individual sequence provides a benefit that decreases with increasing sequence population size. Maintaining a sequence population of stable size also requires the replication of the sequence population to be costly to the host, otherwise the sequence population size will increase indefinitely. Surprisingly, in regimes with high hgt rates, the benefit conferred by the sequence population does not have to exceed the damage it causes to its host. Our analyses provide a plausible scenario for the persistence of sequence populations in bacterial genomes. We also hypothesize a limited biologically relevant parameter range for the provided benefit, which can be tested in future experiments.
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Affiliation(s)
- Hye Jin Park
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, 24306, Germany.,Asia Pacific Center for Theoretical Physics, Pohang, 37673, Korea.,Department of Physics, POSTECH, Pohang, 37673, Korea
| | - Chaitanya S Gokhale
- Research Group for Theoretical Models of Eco-evolutionary Dynamics, Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, 24306, Germany
| | - Frederic Bertels
- Research Group for Microbial Molecular Evolution, Department of Microbial Population Biology, Max Planck Institute for Evolutionary Biology, Plön, 24306, Germany
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13
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Nag Chowdhury S, Kundu S, Banerjee J, Perc M, Ghosh D. Eco-evolutionary dynamics of cooperation in the presence of policing. J Theor Biol 2021; 518:110606. [PMID: 33582077 DOI: 10.1016/j.jtbi.2021.110606] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Revised: 12/31/2020] [Accepted: 01/24/2021] [Indexed: 11/15/2022]
Abstract
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.
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Affiliation(s)
- Sayantan Nag Chowdhury
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Jeet Banerjee
- BYJU'S, Think & Learn Pvt. Ltd., IBC Knowledge Park, 4/1 Bannerghatta Main Road, Bangalore 560029, India.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria.
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
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14
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Wang X, Fu F. Eco-evolutionary dynamics with environmental feedback: Cooperation in a changing world. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/132/10001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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15
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Argasinski K, Rudnicki R. Replicator dynamics for the game theoretic selection models based on state. J Theor Biol 2020; 526:110540. [PMID: 33221278 DOI: 10.1016/j.jtbi.2020.110540] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 11/06/2020] [Accepted: 11/10/2020] [Indexed: 11/16/2022]
Abstract
The paper presents an attempt to integrate the classical evolutionary game theory based on replicator dynamics and the state-based approach of Houston and McNamara. In the new approach, individuals have different heritable strategies; however, individuals carrying the same strategy can differ in terms of state, role or the situation in which they act. Thus, the classical replicator dynamics is completed by the additional subsystem of differential equations describing the dynamics of transitions between different states. In effect, the interactions described by game structure, in addition to the demographic payoffs (constituted by births and deaths), can lead to the change in state of the competing individuals. Special cases of reversible and irreversible incremental stage-structured models, where the state changes can describeenergy accumulation, developmental steps or aging, are derived for discrete and continuous versions. The new approach is illustrated using the example of the Owner-Intruder game with explicit dynamics of the role changes. The new model presents a generalization of the demographic version of the Hawk-Dove game,with the difference being that the opponents in the game are drawn from two separate subpopulations consisting of Owners and Intruders. Here, the Intruders check random nest sites and play the Hawk-Dove game with the Owner if they are occupied. Meanwhile, the Owners produce newborns that become Intruders, since they must find a free nest site to reproduce. An interesting feedback mechanism is produced via the fluxes of individuals between the different subpopulations. In addition, the population growth suppression mechanism resulting from the fixation Bourgeois strategy is analyzed.
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Affiliation(s)
- Krzysztof Argasinski
- Institute of Mathematics of Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland.
| | - Ryszard Rudnicki
- Institute of Mathematics of Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland.
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16
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Shibasaki S, Mitri S. Controlling evolutionary dynamics to optimize microbial bioremediation. Evol Appl 2020; 13:2460-2471. [PMID: 33005234 PMCID: PMC7513707 DOI: 10.1111/eva.13050] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Revised: 06/03/2020] [Accepted: 06/22/2020] [Indexed: 12/24/2022] Open
Abstract
Some microbes have a fascinating ability to degrade compounds that are toxic for humans in a process called bioremediation. Although these traits help microbes survive the toxins, carrying them can be costly if the benefit of detoxification is shared by all surrounding microbes, whether they detoxify or not. Detoxification can thereby be seen as a public goods game, where nondegrading mutants can sweep through the population and collapse bioremediation. Here, we constructed an evolutionary game theoretical model to optimize bioremediation in a chemostat initially containing "cooperating" (detoxifying) microbes. We consider two types of mutants: "cheaters" that do not detoxify, and mutants that become resistant to the toxin through private mechanisms that do not benefit others. By manipulating the concentration and flow rate of a toxin into the chemostat, we identified conditions where cooperators can exclude cheaters that differ in their private resistance. However, eventually, cheaters are bound to invade. To overcome this inevitable outcome and maximize detoxification efficiency, cooperators can be periodically reinoculated into the population. Our study investigates the outcome of an evolutionary game combining both public and private goods and demonstrates how environmental parameters can be used to control evolutionary dynamics in practical applications.
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Affiliation(s)
- Shota Shibasaki
- Department of Fundamental MicrobiologyUniversity of LausanneLausanneSwitzerland
| | - Sara Mitri
- Department of Fundamental MicrobiologyUniversity of LausanneLausanneSwitzerland
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17
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Taitelbaum A, West R, Assaf M, Mobilia M. Population Dynamics in a Changing Environment: Random versus Periodic Switching. PHYSICAL REVIEW LETTERS 2020; 125:048105. [PMID: 32794803 DOI: 10.1103/physrevlett.125.048105] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Revised: 05/13/2020] [Accepted: 06/23/2020] [Indexed: 06/11/2023]
Abstract
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.
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Affiliation(s)
- Ami Taitelbaum
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Robert West
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Michael Assaf
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Mauro Mobilia
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
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18
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Yamamichi M, Kyogoku D, Iritani R, Kobayashi K, Takahashi Y, Tsurui-Sato K, Yamawo A, Dobata S, Tsuji K, Kondoh M. Intraspecific Adaptation Load: A Mechanism for Species Coexistence. Trends Ecol Evol 2020; 35:897-907. [PMID: 32674869 DOI: 10.1016/j.tree.2020.05.011] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2019] [Revised: 05/22/2020] [Accepted: 05/28/2020] [Indexed: 12/13/2022]
Abstract
Evolutionary ecological theory suggests that selection arising from interactions with conspecifics, such as sexual and kin selection, may result in evolution of intraspecific conflicts and evolutionary 'tragedy of the commons'. Here, we propose that such an evolution of conspecific conflicts may affect population dynamics in a way that enhances species coexistence. Empirical evidence and theoretical models suggest that more abundant species is more susceptible to invasion of 'selfish' individuals that increase their own reproductive success at the expense of population growth (intraspecific adaptation load). The density-dependent intraspecific adaptation load gives rise to a self-regulation mechanism at the population level, and stabilizes species coexistence at the community level by negative frequency-dependence.
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Affiliation(s)
- Masato Yamamichi
- Department of General Systems Studies, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan.
| | - Daisuke Kyogoku
- Faculty of Agriculture, Ryukoku University, 1-5 Yokotani, Seta Oe-cho, Otsu, Shiga 520-2194, Japan
| | - Ryosuke Iritani
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), Wako, Saitama 351-0198, Japan
| | - Kazuya Kobayashi
- Hokkaido Forest Research Station, Field Science Education and Research Center, Kyoto University, 553 Tawa, Shibecha-cho, Kawakami-gun, Hokkaido 088-2339, Japan
| | - Yuma Takahashi
- Department of Biology, Faculty of Science, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan
| | - Kaori Tsurui-Sato
- Center for Strategic Research Project, University of the Ryukyus, Senbaru, Nishihara, Okinawa 903-0213, Japan
| | - Akira Yamawo
- Faculty of Agriculture and Life Science, Hirosaki University, 1 Bunkyo-cho, Hirosaki 036-8560, Japan
| | - Shigeto Dobata
- Laboratory of Insect Ecology, Graduate School of Agriculture, Kyoto University, Kitashirakawa-oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kazuki Tsuji
- Department of Subtropical Agro-Environmental Sciences, Faculty of Agriculture, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan
| | - Michio Kondoh
- Graduate School of Life Sciences, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan.
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19
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Synthetic Symbiosis under Environmental Disturbances. mSystems 2020; 5:5/3/e00187-20. [PMID: 32546669 PMCID: PMC7300358 DOI: 10.1128/msystems.00187-20] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The power of synthetic biology is immense. Will it, however, be able to withstand the environmental pressures once released in the wild. As new technologies aim to do precisely the same, we use a much simpler model to test mathematically the effect of a changing environment on a synthetic biological system. We assume that the system is successful if it maintains proportions close to what we observe in the laboratory. Extreme deviations from the expected equilibrium are possible as the environment changes. Our study provides the conditions and the designer specifications which may need to be incorporated in the synthetic systems if we want such “ecoblocs” to survive in the wild. By virtue of complex ecologies, the behavior of mutualisms is challenging to study and nearly impossible to predict. However, laboratory engineered mutualistic systems facilitate a better understanding of their bare essentials. On the basis of an abstract theoretical model and a modifiable experimental yeast system, we explore the environmental limits of self-organized cooperation based on the production and use of specific metabolites. We develop and test the assumptions and stability of the theoretical model by leveraging the simplicity of an artificial yeast system as a simple model of mutualism. We examine how one-off, recurring, and permanent changes to an ecological niche affect a cooperative interaction and change the population composition of an engineered mutualistic system. Moreover, we explore how the cellular burden of cooperating influences the stability of mutualism and how environmental changes shape this stability. Our results highlight the fragility of mutualisms and suggest interventions, including those that rely on the use of synthetic biology. IMPORTANCE The power of synthetic biology is immense. Will it, however, be able to withstand the environmental pressures once released in the wild. As new technologies aim to do precisely the same, we use a much simpler model to test mathematically the effect of a changing environment on a synthetic biological system. We assume that the system is successful if it maintains proportions close to what we observe in the laboratory. Extreme deviations from the expected equilibrium are possible as the environment changes. Our study provides the conditions and the designer specifications which may need to be incorporated in the synthetic systems if we want such “ecoblocs” to survive in the wild.
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20
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Henriques GJB, Osmond MM. Cooperation can promote rescue or lead to evolutionary suicide during environmental change. Evolution 2020; 74:1255-1273. [PMID: 32614158 DOI: 10.1111/evo.14028] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Revised: 02/05/2020] [Accepted: 05/23/2020] [Indexed: 12/20/2022]
Abstract
The adaptation of populations to changing conditions may be affected by interactions between individuals. For example, when cooperative interactions increase fecundity, they may allow populations to maintain high densities and thus keep track of moving environmental optima. Simultaneously, changes in population density alter the marginal benefits of cooperative investments, creating a feedback loop between population dynamics and the evolution of cooperation. Here we model how the evolution of cooperation interacts with adaptation to changing environments. We hypothesize that environmental change lowers population size and thus promotes the evolution of cooperation, and that this, in turn, helps the population keep up with the moving optimum. However, we find that the evolution of cooperation can have qualitatively different effects, depending on which fitness component is reduced by the costs of cooperation. If the costs decrease fecundity, cooperation indeed speeds adaptation by increasing population density; if, in contrast, the costs decrease viability, cooperation may instead slow adaptation by lowering the effective population size, leading to evolutionary suicide. Thus, cooperation can either promote or-counterintuitively-hinder adaptation to a changing environment. Finally, we show that our model can also be generalized to other social interactions by discussing the evolution of competition during environmental change.
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Affiliation(s)
- Gil J B Henriques
- Department of Zoology, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada
| | - Matthew M Osmond
- Center for Population Biology, University of California, Davis, Davis, California, 95616
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21
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Pichugin Y, Park HJ, Traulsen A. Evolution of simple multicellular life cycles in dynamic environments. J R Soc Interface 2020; 16:20190054. [PMID: 31088261 DOI: 10.1098/rsif.2019.0054] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The mode of reproduction is a critical characteristic of any species, as it has a strong effect on its evolution. As any other trait, the reproduction mode is subject to natural selection and may adapt to the environment. When the environment varies over time, different reproduction modes could be optimal at different times. The natural response to a dynamic environment seems to be bet hedging, where multiple reproductive strategies are stochastically executed. Here, we develop a framework for the evolution of simple multicellular life cycles in a dynamic environment. We use a matrix population model of undifferentiated multicellular groups undergoing fragmentation and ask which mode maximizes the population growth rate. Counterintuitively, we find that natural selection in dynamic environments generally tends to promote deterministic, not stochastic, reproduction modes.
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Affiliation(s)
- Yuriy Pichugin
- Max Planck Institute for Evolutionary Biology , August-Thienemann-Strasse 2, Plön 24306 , Germany
| | - Hye Jin Park
- Max Planck Institute for Evolutionary Biology , August-Thienemann-Strasse 2, Plön 24306 , Germany
| | - Arne Traulsen
- Max Planck Institute for Evolutionary Biology , August-Thienemann-Strasse 2, Plön 24306 , Germany
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22
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Abstract
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceeds [Formula: see text], where k is the average number of neighbors of an individual and [Formula: see text] captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.
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Affiliation(s)
- Qi Su
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138
| | - Alex McAvoy
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138;
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China;
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138;
- Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138
- Department of Mathematics, Harvard University, Cambridge, MA 02138
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23
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Shibasaki S. The evolutionary game of interspecific mutualism in the multi-species model. J Theor Biol 2019; 471:51-58. [PMID: 30935957 DOI: 10.1016/j.jtbi.2019.03.026] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2018] [Revised: 03/26/2019] [Accepted: 03/28/2019] [Indexed: 11/30/2022]
Abstract
Mutualistic interspecific interactions, including Müllerian mimicry and division of labor, are common in nature. In contrast to antagonistic interactions, where faster evolution is favored, mutualism can favor slower evolution under certain conditions. This is called the Red King effect. Since Bergstrom and Lachmann (2003) proposed the Red King effect, it has been investigated only in two-species models. However, biological examples suggest that mutualism can include three or more species. Here, I modeled the evolutionary dynamics of mutualism in communities where involving two or more species, and in which all species mutually interact. Regardless of the number of species in the community, it is possible to derive conditions for stable equilibria. Although nonlinear relationships exist between the evolutionary rates and the evolutionary fate of each species in the multi-species communities, the model suggests that it is possible to predict whether faster evolution is favored or disfavored for the relatively rapidly evolving species; however, it is difficult to predict the evolutionary fate of species that evolve relatively slowly because their evolutionary dynamics are affected by the evolutionary fate of species evolving rapidly.
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Affiliation(s)
- Shota Shibasaki
- Department of General Systems Studies, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, 1538902, Japan; Department of Fundamental Microbiology, University of Lausanne, Quartier UNIL-Sorge, CH-1015 Lausanne, Switzerland.
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24
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Park HJ, Pichugin Y, Huang W, Traulsen A. Population size changes and extinction risk of populations driven by mutant interactors. Phys Rev E 2019; 99:022305. [PMID: 30934279 DOI: 10.1103/physreve.99.022305] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2018] [Indexed: 11/07/2022]
Abstract
Spontaneous random mutations are an important source of variation in populations. Many evolutionary models consider mutants with a fixed fitness, chosen from a fitness distribution without considering microscopic interactions among the residents and mutants. Here, we go beyond this and consider "mutant interactors," which lead to new interactions between the residents and invading mutants that can affect the population size and the extinction risk of populations. We model microscopic interactions between individuals by using a dynamic interaction matrix, the dimension of which increases with the emergence of a new mutant and decreases with extinction. The new interaction parameters of the mutant follow a probability distribution around the payoff entries of its ancestor. These new interactions can drive the population away from the previous equilibrium and lead to changes in the population size. Thus, the population size is an evolving property rather than an externally controlled variable. We calculate the average population size of our stochastic system over time and quantify the extinction risk of the population by the mean time to extinction.
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Affiliation(s)
- Hye Jin Park
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
| | - Yuriy Pichugin
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
| | - Weini Huang
- Complex Systems and Networks Research Group, School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.,Group of Theoretical Biology, The State Key Laboratory of Biocontrol, School of Life Science, Sun Yat-sen University, Guangzhou 510060, China
| | - Arne Traulsen
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany
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25
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Patel M, Raymond B, Bonsall MB, West SA. Crystal toxins and the volunteer's dilemma in bacteria. J Evol Biol 2019; 32:310-319. [PMID: 30672052 PMCID: PMC6487926 DOI: 10.1111/jeb.13415] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Revised: 01/11/2019] [Accepted: 01/15/2019] [Indexed: 11/28/2022]
Abstract
The growth and virulence of the bacteria Bacillus thuringiensis depend on the production of Cry toxins, which are used to perforate the gut of its host. Successful invasion of the host relies on producing a threshold amount of toxin, after which there is no benefit from producing more toxin. Consequently, the production of Cry toxin appears to be a different type of social problem compared with the public goods scenarios that bacteria usually encounter. We show that selection for toxin production is a volunteer's dilemma. We make specific predictions that (a) selection for toxin production depends upon an interplay between the number of bacterial cells that each host ingests and the genetic relatedness between those cells; (b) cheats that do not produce toxin gain an advantage when at low frequencies, and at high bacterial density, allowing them to be maintained in a population alongside toxin‐producing cells. More generally, our results emphasize the diversity of the social games that bacteria play.
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Affiliation(s)
| | - Ben Raymond
- College of Life and Environmental Science, University of Exeter, Penryn, Cornwall, UK
| | | | - Stuart A West
- Department of Zoology, University of Oxford, Oxford, UK
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26
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Hauert C, Saade C, McAvoy A. Asymmetric evolutionary games with environmental feedback. J Theor Biol 2019; 462:347-360. [DOI: 10.1016/j.jtbi.2018.11.019] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2018] [Revised: 11/18/2018] [Accepted: 11/20/2018] [Indexed: 10/27/2022]
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27
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Park HJ, Gokhale CS. Ecological feedback on diffusion dynamics. ROYAL SOCIETY OPEN SCIENCE 2019; 6:181273. [PMID: 30891264 PMCID: PMC6408370 DOI: 10.1098/rsos.181273] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Accepted: 01/09/2019] [Indexed: 06/09/2023]
Abstract
Spatial patterns are ubiquitous across different scales of organization in ecological systems. Animal coat pattern, spatial organization of insect colonies and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction-diffusion equations, which consider individuals dispersing between subpopulations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. Furthermore, we show how these evolutionary dynamics feed back into shaping the ecology, thus together determining the fate of the system.
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Affiliation(s)
- Hye Jin Park
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August Thienemann Street 2, 24306 Plön, Germany
| | - Chaitanya S. Gokhale
- Research Group for Theoretical Models of Eco-evolutionary Dynamics, Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August Thienemann Street 2, 24306 Plön, Germany
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28
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Govaert L, Fronhofer EA, Lion S, Eizaguirre C, Bonte D, Egas M, Hendry AP, De Brito Martins A, Melián CJ, Raeymaekers JAM, Ratikainen II, Saether B, Schweitzer JA, Matthews B. Eco‐evolutionary feedbacks—Theoretical models and perspectives. Funct Ecol 2018. [DOI: 10.1111/1365-2435.13241] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Lynn Govaert
- Laboratory of Aquatic Ecology, Evolution and Conservation KU Leuven Leuven Belgium
- Department of Aquatic Ecology Eawag: Swiss Federal Institute of Aquatic Science and Technology Dübendorf Switzerland
- Department of Evolutionary Biology and Environmental Studies University of Zurich Zürich Switzerland
| | | | - Sébastien Lion
- Centre d'Ecologie Fonctionnelle et Evolutive CNRS, IRD, EPHE Université de Montpellier Montpellier France
| | | | - Dries Bonte
- Department of Biology Ghent University Ghent Belgium
| | - Martijn Egas
- Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam The Netherlands
| | - Andrew P. Hendry
- Redpath Museum and Department of Biology McGill University Montreal Quebec Canada
| | - Ayana De Brito Martins
- Fish Ecology and Evolution DepartmentCenter for Ecology, Evolution and BiogeochemistryEawag: Swiss Federal Institute of Aquatic Science and Technology Dübendorf Switzerland
| | - Carlos J. Melián
- Fish Ecology and Evolution DepartmentCenter for Ecology, Evolution and BiogeochemistryEawag: Swiss Federal Institute of Aquatic Science and Technology Dübendorf Switzerland
| | | | - Irja I. Ratikainen
- Department of Biology Centre for Biodiversity Dynamics Norwegian University of Science and Technology Trondheim Norway
- Institute of Biodiversity, Animal Health and Comparative Medicine University of Glasgow Glasgow UK
| | - Bernt‐Erik Saether
- Department of Biology Centre for Biodiversity Dynamics Norwegian University of Science and Technology Trondheim Norway
| | - Jennifer A. Schweitzer
- Department of Ecology and Evolutionary Biology University of Tennessee Knoxville Tennessee
| | - Blake Matthews
- Department of Aquatic Ecology Eawag: Swiss Federal Institute of Aquatic Science and Technology Dübendorf Switzerland
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29
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Disentangling eco-evolutionary effects on trait fixation. Theor Popul Biol 2018; 124:93-107. [PMID: 30359662 DOI: 10.1016/j.tpb.2018.10.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2018] [Revised: 10/08/2018] [Accepted: 10/11/2018] [Indexed: 11/23/2022]
Abstract
In population genetics, fixation of traits in a demographically changing population under frequency-independent selection has been extensively analysed. In evolutionary game theory, models of fixation have typically focused on fixed population sizes and frequency-dependent selection. A combination of demographic fluctuations with frequency-dependent interactions such as Lotka-Volterra dynamics has received comparatively little attention. We consider a stochastic, competitive Lotka-Volterra model with higher order interactions between two traits. The emerging individual-based model allows for stochastic fluctuations in the frequencies of the two traits and the total population size. We calculate the fixation probability of a trait under differing competition coefficients. This fixation probability resembles, qualitatively, the deterministic evolutionary dynamics. Furthermore, we partially disentangle the selection effects into their ecological and evolutionary components. We find that changing the evolutionary selection strength also changes the population dynamics and vice versa. Thus, a clean separation of the ecological and evolutionary effects is not possible. Instead, our results imply a nested interaction of the evolutionary and ecological effects. The entangled eco-evolutionary processes thus cannot be ignored when determining fixation properties in a co-evolutionary system.
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30
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Hilbe C, Šimsa Š, Chatterjee K, Nowak MA. Evolution of cooperation in stochastic games. Nature 2018; 559:246-249. [PMID: 29973718 DOI: 10.1038/s41586-018-0277-x] [Citation(s) in RCA: 66] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Accepted: 05/17/2018] [Indexed: 11/09/2022]
Abstract
Social dilemmas occur when incentives for individuals are misaligned with group interests1-7. According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory8. The theory of direct reciprocity9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment-either naturally occurring or designed-help to overcome social dilemmas.
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Affiliation(s)
- Christian Hilbe
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA. .,IST Austria, Klosterneuburg, Austria.
| | - Štěpán Šimsa
- Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
| | | | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA. .,Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA, USA.
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31
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Argasinski K, Broom M. Evolutionary stability under limited population growth: Eco-evolutionary feedbacks and replicator dynamics. ECOLOGICAL COMPLEXITY 2018. [DOI: 10.1016/j.ecocom.2017.04.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Argasinski K, Broom M. Interaction rates, vital rates, background fitness and replicator dynamics: how to embed evolutionary game structure into realistic population dynamics. Theory Biosci 2018; 137:33-50. [PMID: 29159683 PMCID: PMC5893772 DOI: 10.1007/s12064-017-0257-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2016] [Accepted: 10/16/2017] [Indexed: 11/13/2022]
Abstract
In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction events in time, which seriously affects the population dynamics, as is shown in this paper. This leads to the model of a population of individuals playing different games, where focal game affected by the considered trait can be extracted from the general model, and the impact on the dynamics of other events (which is not neutral) can be described by an average background fertility and mortality. This leads to a distinction between two types of background fitness, strategically neutral elements of the focal games (correlated with the focal game events) and the aggregated outcomes of other interactions (independent of the focal game). The new approach is useful for clarification of the biological meaning of concepts such as weak selection. Results are illustrated by a Hawk-Dove example.
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Affiliation(s)
- K. Argasinski
- Institute of Mathematics of Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa 10, Poland
| | - M. Broom
- Department of Mathematics, City, University of London, Northampton Square, London, EC1V 0HB UK
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Stollmeier F, Nagler J. Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs. PHYSICAL REVIEW LETTERS 2018; 120:058101. [PMID: 29481174 DOI: 10.1103/physrevlett.120.058101] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Indexed: 06/08/2023]
Abstract
Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair," meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the prisoner's dilemma, and an unexpected selection reversal in the hawk-dove game.
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Affiliation(s)
- Frank Stollmeier
- Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, Am Faßberg 17, 37077 Göttingen, Germany
| | - Jan Nagler
- Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH 8093 Zurich, Switzerland
- Computational Social Science, Department of Humanities, Social and Political Sciences, ETH Zurich, Clausiusstrasse 50, CH-8092 Zurich, Switzerland
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De Jaegher K. Harsh environments and the evolution of multi-player cooperation. Theor Popul Biol 2016; 113:1-12. [PMID: 27664440 DOI: 10.1016/j.tpb.2016.09.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Revised: 08/31/2016] [Accepted: 09/10/2016] [Indexed: 12/22/2022]
Abstract
The game-theoretic model in this paper provides micro-foundations for the effect a harsher environment on the probability of cooperation among multiple players. The harshness of the environment is alternatively measured by the degree of complementarity between the players' cooperative efforts in producing a public good, and by the number of attacks on an existing public good that the players can collectively defend, where it is shown that these two measures of the degree of adversity facing the players operate in a similar fashion. We show that the effect of the degree of adversity on the probability of cooperation is monotonous, and has an opposite sign for smaller and for larger cooperation costs. For intermediate cooperation costs, we show that the effect of a harsher environment on the probability of cooperation is hill-shaped.
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Affiliation(s)
- Kris De Jaegher
- Utrecht University School of Economics, Utrecht University, Kriekenpitplein 21-22, 3584 EC, Utrecht, The Netherlands.
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